Stabilization of Nonlinear Systems Using Event-Triggered Output Feedback Controllers

Abstract

Abstract-The objective is to design output feedback event-triggered controllers to stabilize a class of nonlinear systems. One of the main difficulties of the problem is to ensure the existence of a minimum amount of time between two consecutive transmissions, which is essential in practice. We solve this issue by combining techniques from eventtriggered and time-triggered control. The idea is to turn on the eventtriggering mechanism only after a fixed amount of time has elapsed since the last transmission. This time is computed based on results on the stabilization of time-driven sampled-data systems. The overall strategy ensures an asymptotic stability property for the closed-loop system. The results are proved to be applicable to linear time-invariant (LTI) systems as a particular case.

Periodic event-triggered control of nonlinear systems using overapproximation techniques

“…Assumption 1 holds for most CETC designs proposed in literature, including [1,5,7,11,13,15,16,22,24,25]. It implies that the set Ω is forward invariant for the closedloop CETC system (3) (i.e., that all solutions starting in Ω remain in Ω for all t ∈ R 0 ), and rules out finite escape times and Zeno-behaviour (an infinite number of events in a finite time interval) that would prevent global existence of all solutions starting in Ω.…”

“…Sufficient conditions for this assumption to hold are given in [22], and most available event-triggering schemes in the literature either provide a positive lower bound on T (e.g., [7,22,24]), or enforce a positive lower bound by design (e.g., [1,5,22,25]). …”

“…(2) We do not require that the set Ω is compact, see Assumption 1. As a result, we can now also apply our PETC design to CETC systems which have additional variables in the event-generator that are not forward invariant with regard to any compact set, such as timers or counters (see, e.g., [1,5,22,25]). (3) We do not require that all solutions z(t, z(t s j )) tȯ z = g(z) lie inside Ω for all t ∈ [0, h].…”

“…We design a continuous event-triggering condition as in [1]. The idea is to wait a fixed amount of time T > 0 before checking a state-dependent criterion of the same form as in [24].…”

“…To constructΓ, we have verified that the conditions required in [1] hold, by following similar lines as in [19,Example 1]. We have taken the Lyapunov function…”